Origin of the singular Bethe ansatz solutions for the Heisenberg XXZ spin chain

Jae Dong Noh, Deok-Sun Lee and Doochul Kim

Physica A: Statistical Mechanics and its Applications, 2000, vol. 287, issue 1, 167-176

Abstract: We investigate symmetry properties of the Bethe ansatz wave functions for the Heisenberg XXZ spin chain. The XXZ Hamiltonian commutes simultaneously with the shift operator T and the lattice inversion operator V in the space of Ω=±1 with Ω the eigenvalue of T. We show that the Bethe ansatz solutions with normalizable wave functions cannot be the eigenstates of T and V with quantum number (Ω,ϒ)=(±1,∓1) where ϒ is the eigenvalue of V. Therefore, the Bethe ansatz wave functions should be singular for nondegenerate eigenstates of the Hamiltonian with quantum number (Ω,ϒ)=(±1,∓1). It is also shown that such states exist in any nontrivial down-spin number sector and that the number of them diverges exponentially with the chain length.

Keywords: Heisenberg XXZ spin chain; Singular Bethe ansatz solution; Symmetry (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:287:y:2000:i:1:p:167-176

DOI: 10.1016/S0378-4371(00)00450-7

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